Complex NumbersEasy
Question
Let α, β be real and z be a complex number. If z2 + αz + β = 0 has two distinct roots on the line Rez = 1, then it is necessary that
Options
A.β ∈ ( - 1, 0)
B.|β| = 1
C.β ∈ (1, ∝)
D.β ∈ (0, 1)
Solution
Suppose roots are 1+ pi, 1+ qi
Sum of roots 1+ pi +1+ qi = - α which is real
⇒ roots of 1+ pi, 1 - pi
Product of roots = β = 1 + p2 ∈ (1, ∞)
p ≠ 0 since roots are distinct.
Sum of roots 1+ pi +1+ qi = - α which is real
⇒ roots of 1+ pi, 1 - pi
Product of roots = β = 1 + p2 ∈ (1, ∞)
p ≠ 0 since roots are distinct.
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